The geometry of bicharacteristics and the global existence of holomorphic solutions of systems of linear differential equations (Q1191320)

(From the author's introduction:) When we study the existence of holomorphic solutions, we should consider the Cauchy-Riemann equations together with the linear differential equations under consideration. Then, due to the Cauchy-Riemann equations, we can apply the theory of boundary value problems for elliptic systems developed by Kashiwara- Kawai. In fact, making use of this theory with a result of Sato-Kawai- Kashiwara, Kawai has presented some theorems on finite-dimensionality of cohomology groups attached to elliptic systems. In the situation we are considering, his results give sufficient conditions which guarantee the (semi-) global existence of holomorphic solutions. We investigate the geometric meaning of his conditions, supposing the second order tangency of the bicharacteristics and the boundary of the domain in question. As a result we can obtain our main theorems which describe the relationship between the geometry of bicharacteristics and the (semi-) global existence of holomorphic solutions.